Filtering of Time-Varying Nonlinear Systems with Randomly Occurring Output Degradation

This paper deals with the filtering problem for nonlinear systems with randomly occurring output degradation phenomenon. Such a phenomenon is described by a stochastic variable which obeys the Bernoulli distribution with probability known priorly. A sufficient condition is derived for the nonlinear system to reach the required performance. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method. 1. Introduction Many practical engineering systems, like the radar systems which are used for tracking the hostile weapon systems, are always encountering failures. For example, the radar systems will fail from time to time due to the electromagnetic interference from the enemy. Moreover, other reasons that lead the sensors to failures mainly include the external disturbance and changes of working conditions, to name just a few; see [1–3], for example. It is worth pointing out that, in the systems mentioned above, the sensor failure is not persistent all the time but is intermittent stochastically. In other words, the sensor failure occurs at random time points in a probabilistic way. Such phenomena are called the randomly occurring phenomena which would drastically degrade the system performance. Therefore, in recent years, the randomly occurring phenomena have stirred quite a lot of research interests due to its clear engineering insights and many results have been reported in the literature; see [4–11] for some latest publications. However, in spite of its clear physical insight and importance in engineering application, the filtering problem for nonlinear time-varying systems under the circumstance of randomly occurring output degradation has not yet been studied sufficiently. On another research frontier, it is well known that the nonlinearities are inevitable in practical engineering systems, and the analysis and synthesis of nonlinear systems have been attracting more and more research attention, among which the sector bound nonlinearity which could cover several class of well-studied nonlinearities has drawn particular research focus since many sensor failures like missing measurements, signal saturations can be easily converted into the nonlinearity belonging to a known sector; see [11–15] and the references therein. On the other hand, in recent years, time-varying systems have started to receive attention due to the fact that there are virtually no strictly time-invariant systems since the